Geodesic
The Scalar Curvature of the Tangent Bundle with Special Almost Product Metric
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 178-182

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We study a class of Riemannian metrics $\widetilde g$ on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$ which contains, in particular, the Sasaki and the Cheeger–Gromoll metrics. In the case when $(M,g)$ is a space of constant section curvature $k$, we find conditions under which the scalar curvature $\widetilde S$ of $(TM,\widetilde g)$ is constant.
Keywords: almost product structure, tangent bundle, Riemannian metric, sectional curvature, scalar curvature. 
O. V. Sukhova. The Scalar Curvature of the Tangent Bundle with Special Almost Product Metric. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 178-182. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a14/
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